2x^2-x-17=-5

Solution for 2x^2-x-17=-5 equation:

2x^2-x-17=-5

We move all terms to the left:

2x^2-x-17-(-5)=0

We add all the numbers together, and all the variables

2x^2-1x-12=0

a = 2; b = -1; c = -12;
Δ = b2-4ac
Δ = -12-4·2·(-12)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{97}}{2*2}=\frac{1-\sqrt{97}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*2}=\frac{1+\sqrt{97}}{4}
$